GENERALIZED SEMIDERIVATIONS IN PRIME RINGS WITH ALGEBRAIC IDENTITIES.

Let R be a prime ring with center Z(R). Suppose that R admits a generalized semiderivation F with associated derivation d 6= 0. In the present paper we investigate the commutativity of a prime ring R satisfying any one of the identities: (i) F([x; y]) 2 Z(R), (ii) F(x-y) 2 Z(R), (iii) F(xy)-xy 2 Z(R), (iv) F(xy) - yx 2 Z(R), (v) [F(x); F(y)] = 0; (vi) F(x) - F(y) = 0 for all x; y 2 R. [ABSTRACT FROM AUTHOR]